Research on Model-based Predictive Control (MPC) associated with theoretical work and practical applications has flourished over the past 30 years. A broad body of literature and a number of survey papers attest to this fact (Lee, 2011; Qin & Badgwell, 2003). MPC algorithms display a number of desirable features that enable them to be robust. They can perform in the presence of nonlinearities and modeling errors and can handle constraints and multi-variable plants (Diehl, Amrit, & Rawlings, 2011; Runzi & Low, 2009). As the field of MPC is an ongoing area of research, recent developments on new MPC algorithms include M-Shifted, extended predictive control, fast MPC, and latent variable MPC (Abu-Ayyad & Dubay, 2006; Dubay, Kember, Lakshminarayan, & Pramujati, 2006; Jesus & MacGregor, 2005). This in combination with advancements in the computer industry have allowed the MPC algorithm to extend to applications requiring small sampling times (Bolognani, Peretti, & Zigliotto, 2009; Diehl et al., 2011).
Early application of MPC algorithms to the process industry were generally subjected to relatively simple reference or setpoint trajectories. In standard applications the reference often settles at a fixed setpoint such as a temperature, a fluid level, or a speed in the case of motor speed control. The MPC methodology has been recently introduced to applications that include the field of robotics and Unmanned Aerial Vehicles (UAV) (Gregor & Skrjanc, 2007; Kim & Shim, 2003; Ren & Beard, 2004). Other current applications of MPC schemes include flexible manipulators (Hassan, Dubay, Li, & Wang, 2007) and plastic injection molding (Dubay, Pramujati, Han, & Strohmaier, 2007). In these cases the desired reference trajectories can be more complex. Standard MPC algorithms exhibit difficulty when tracking complex profiles (Golshan, MacGregor, Bruwer, & Mhaskar, 2010).
Little work has been done in terms of complex reference tracking with MPC control. It is becoming increasingly important for advanced control schemes to be able to track more complex reference trajectories for more efficient control (Ali, Yu, & Hauser, 2001; Mayne, Rawlings, Rao, & Scokaert, 2000). From an industrial perspective, tighter trajectory tracking can lead to better part quality and energy consumption. Latent variable MPC is one algorithm that has been recently designed in order to optimize trajectory tracking performance (Jesus & MacGregor, 2005). The latent variable scheme has successfully been applied to batch processes (Golshan et al., 2010; Lauri, Rossiter, Sanchisa, & Martineza, 2010). The method is an effective solution to the complex trajectory tracking problem but cannot be readily adapted to common or conventional forms of MPC.
The tracking offset apparent when tracking complex reference trajectories is identified as a result of the open loop system time constants that are not accounted for in controller prediction formulations. Different methods to correct steady state offset due to disturbance or model mismatch have been developed (Magni & Scattolini, 2005; Rawlings & Mayne, 2009). These methods have been designed for constant reference trajectory tracking and do not eliminate the offset tracking that exists when tracking slopes. Evidence of the complex trajectory tracking offset problem can be seen in Yang and Gao (2000), Dubay et al. (2007), Dalarnagkidis, Valavanis, and Piegl (2011), and Li, Su, Shao-Hsien Liu, and Chen (2012).